The Raviart-Thomas family is an important class of finite elements used to describe two-dimensional vector fields.
These elements were introduced for both triangular and quadrilateral elements by [1]}, who used them to solve the Poisson equation with a mixed finite element discretisation.
The Raviart-Thomas elements come in two varieties: those that preserve the normal components of vectors between cells, and those that preserve the tangential components.
These former elements (preserving normal components) are known as \(H(\mathrm {div})\) -conforming as functions in these elements have square-integrable divergence.
The latter (preserving tangential components) are \(H(\mathrm {curl})\) -conforming, which in the context of a two-dimensional manifold means that for all fields \(\mathbf {u}\)  in the corresponding finite element space, \(\mathbf {\nabla }^\perp \mathbf {\cdot u}\)  is square-integrable (as well as \(\mathbf {u}\)  also being square-integrable).
As discussed by [2]}, the quadrilateral Raviart-Thomas elements can be represented as the tensor-product of one-dimensional elements.
For definitions and more thorough descriptions of the elements, see [3]}.
